Why the belt not fitting on body with shrinkwrap?
You should use the 'project' option of the shrinkwrap modifier:



'Nearest surface point' may stretch the mesh to find the closer correspondence to the target.

'Project' projects along the object (belt here) surface's normal until it reaches the target.

Link to the documentation: https://docs.blender.org/manual/fr/dev/modeling/modifiers/deform/shrinkwrap.html#mode

Complement

From there, if you add a solidify, you'll see that the two extremities of the belt overlap.



To avoid that, you'll need to use a vertex group to drive the shrinkwrap. But in this case, you have to apply the mirror modifier first, so that left and right parts can be different:


Apply the mirror
Enter edit mode
Select all the vertices
Create a group and assign the vertices to it
Use this group in the shrinkwrap modifier (the modifier will now use these weights to moderate the influence of the shrinkwrap)




Now, switch to weight paint mode in order to change the vertex group's weights values:


Enter in weight paint mode
Enable vertex selection
Choose/select the vertices on the right (or left)
Choose a substract brush
And tune until the wanted result is obtained